An Intelligent Control Strategy for a Highly Reliable Microgrid in Island Mode

Abstract

An intelligent control strategy based on a membership cloud model in a high reliable off-grid microgrid with a reconfigurable inverter is proposed in this paper. The operating principle of the off-grid microgrid with the reconfigurable inverter is provided, which contains four operating modes. An open-circuit fault diagnosis for the inverter is presented first. The polarities of the midpoint voltages defined in the paper are used to recognize the faulty power switch. The reconfigurable inverter allows the power switches of different bridges to be reconfigured, when there are power switches faulty, to let the inverter operate in faulty state. The working principle of the reconfigurable inverter is given. The membership cloud model with two output channels is built to obtain the virtual impedance to suppress the circulating currents between inverters when the reconfigurable inverter is in faulty state. A pulse resetting method is presented. The general intelligent control strategy for the reconfigurable inverter is formed as the droop-virtual impedance-voltage-current-pulses resetting control. The validity of the intelligent control strategy of the system is verified by simulation.

1. Introduction

Power electronic inverters play more and more important roles in many research fields like motor-driven machines, microgrids, photovoltaics (PVs) and so on [1,2,3,4,5]. One of the basic reasons is the increasing incorporation of direct current (DC)-based renewable energy sources (RES) and storage (PVs and batteries) in the grid, for environmental purposes. Another reason is the ascending DC demand in various infrastructures such as data centers, electric vehicle (EV) charging stations, etc. [6,7,8]. However, the power switches in the inverter are vulnerable to failure for many reasons. Therefore, enhancing the reliability of power electronic inverters becomes more important and has attracted more attention among researchers [9,10].

Real-time fault diagnosis technology is of great significance. In model-based methods, the transient switch voltage signals are analyzed to diagnose the fault quickly [11]. In [12], a new fault feature extraction method based on the trend relationship of adjacent fold lines for data curves is proposed, which can be used to extract the fault features and is not affected by asymmetric interference. When a fault occurs, the currents are distorted. These changes can be used to diagnose the fault [13]. In [14], a current vector instantaneous frequency fault diagnosis method is proposed. It can detect the occurrence of a fault in a very short time, but can’t locate the fault. Wavelet packet transforms and Fourier transforms are used to extract the main components of the signals which can effectively reduce the interference of noise and more clearly identify the types of failures [15,16]. Reference [17] uses rough set theory to detect short-circuit faults of single-phase inverters. It expresses fault signals in the form of 0–1, and directly outputs diagnosis results with electronic devices, which simplifies computation. Knowledge-based methods have been the focus of recent research. These methods can diagnose the faults accurately. In [16], an on-line estimator constituted by a neural network is used to observe system states, and then fault detection and diagnosis is realized. Reference [18] applies fuzzy control to inverter fault diagnosis, which enhances the anti-interference ability of the system and improves the diagnosis accuracy.

In order to allow circuits to operate smoothly after faults, the fault-tolerance of the inverters needs to be considered. Numerous papers discuss fault tolerant methods for the inverters compromising between costs and reliability. The redundant bridge to keep inverters fault-tolerant operating is usually discussed in many studies [19,20,21,22]. These fault-tolerant inverter circuits can output good voltages under faulty conditions. However, the general cost is higher because more redundant power switches are needed in fault-tolerant inverters. The three-phase four-switch (TPFS) topology structure is widely applied because of the advantages of the reduced power switches, such as inverters [23,24], active power filters (APF) [25,26], rectifier [27], and so on. Because of the similarity with the three-phase six-switch (TPSS) structure, the TPFS is proposed as a fault tolerant structure for it [28]. In [29,30], a fault tolerant inverter with the TPFS structure in a microgrid is proposed, which keeps the system operating after cutting the fault power switch devices from the inverter. Reference [31] proposes a finite states model predictive direct power control method for TPFS bidirectional alternating current (AC)/DC converters under unbalanced grid voltage conditions, which can realize the fault tolerant continuous operation of bidirectional AC/DC converters and eliminate active power or reactive power ripples under unbalanced grid voltage conditions with sinusoidal current waveforms.

An intelligent control strategy based on the membership cloud model is proposed and applied in an off-grid microgrid with a reconfigurable inverter in this paper. There are four novel points. First, one of inverters in the off-grid microgrid system is a reconfigurable one, and can be reconfigured twice when it becomes faulty in power switches. Second, the open circuit fault diagnosis method and the reconfiguring method are presented, which both can be applied twice. Third, the principle of the membership cloud model is presented. The circulating currents between two inverters are suppressed by the virtual impedance based on the membership cloud model. Finally, a corresponding control strategy is proposed, which can work in both normal state and faulty state. In particular, when two inverters are both faulty, one inverter is removed, and the remaining inverter is reconfigured to ensure continuous operation of the off-grid microgrid. The fault-tolerant space has been greatly improved.

The paper is organized as follows: The topology structure and four working modes of the off-grid microgrid with the reconfigurable inverter are presented in Section 2. The open-circuit fault diagnosis method and the reconfiguration method for inverter 1 are presented. The controlling strategy of the off-grid microgrid is presented and discussed in this section. The circulating currents between inverters which are suppressed by the virtual impedance based on the membership cloud model are analyzed when the reconfigurable inverter is faulty. A pulse resetting method which is used in the general control strategy of the system is shown. The simulation results are given in Section 3. The final section presents the conclusions.

2. Materials and Methods

2.1. The Off-Grid Microgrid Topology with a Reconfigurable Inverter

The topology structure of the off-grid microgrid with a reconfigurable inverter is shown in Figure 1. The off-grid microgrid contains two inverters. Inverter 1 is the reconfigurable one. V₁–V₆ are power switches. TR₁ TR₂, TR₃ and TR₄ are four triacs. The inductors L₁, L₂ and capacitor C constitute the LCL filter to compensate the harmonics. Inverter 2 is the normal structure with TPSS.

There are four operating modes in the off-grid microgrid in Figure 1. In the operating mode 1, both inverters work in their normal state. TR₃ is kept on while the other triacs are off in inverter 1. In the operating mode 2, inverter 1 works normally, but inverter 2 is detected as faulty by the fault diagnosis method, so it is removed. Both inverters are in faulty operating state in the operating mode 3. Inverter 1 is reconfigured as a TPFS type while inverter 2 is removed. In the operating mode 4, inverter 1 is detected to be faulty and is reconfigured as the TPFS type, while inverter 2 works normally. The four operating modes are shown in

Table 1. Four operating modes.

Modes	Inverter 1	Inverter 2
1	Normal	Normal
2	Normal	Removed
3	TPFS	Removed
4	TPFS	Normal

.

2.2. Open-Circuit Fault Diagnosis and Reconfiguration for Inverter 1

When one of or two of power switches in inverter 1 are faulty, the topology of the inverter 1 will be reconfigured as a three phases four switches (TPFS) structure to keep operating. The corresponding triacs are connected. For example, one of two reconfiguring processes of inverter 1 is shown in Figure 2. Figure 2a is the equivalent circuit for the reconfigurable inverter 1. When V₁ is in open circuit faulty, TR₄ is on and stop trigger V₂. The DC link takes the place of phase c. Then inverter 1 is reconfigured as TPFS as shown in Figure 2d and runs continuously. The first reconfiguration is finished, which is shown in Figure 2b. If V₄ is in open circuit faulty for the reconfigured inverter 1, TR₄ is still on, TR2 on and V₂ takes the place of V₄. The second reconfiguration is finished as shown in Figure 2c and the inverter 1 is reconfigured as TPFS again.

In Figure 2a, u_ao, u_bo, and u_co are the midpoint voltages between the midpoint of the three phase bridge arms and the midpoint of the DC side. The fault characteristics of the midpoint voltages are analyzed after an open-circuit fault occurs in the reconfigurable inverter 1. Then these features are used for fault diagnosis. The fault diagnosis can be used in TPFS and TPSS structures. The bridge switch function S_x is set as:

$$S_x=\left\{\begin{array}{l}1\hspace{1em}\hspace{1em}\mathrm{upper} \mathrm{bridge} \mathrm{on}\\ -1\hspace{1em} \mathrm{lower} \mathrm{bridge} \mathrm{on}\end{array}\right.,$$

(1)

Here phase x = (a, b, c). The midpoint voltage u_xo without fault can be obtained from Figure 2a as:

$$u_{xo}=\frac{u_{dc}}{2}{S}_x,$$

(2)

when V₁ is in an open-circuit fault and S_c = 1, V₁ and V₂ are both disconnected, and c is suspended, then i_c = 0. The potential of point c is equal to that of point n and there is u_coF1 = u_no1. The midpoint voltage u_coF1 after the first fault can be obtained:

$$u_{coF1}=u_{no1}=\frac{u_{ao1}+u_{bo1}}{3}=\frac{u_{dc}}{3}(S_a+S_b)-u_{dc},$$

(3)

Then different S_a and S_b are substituted into the Equation (3), the midpoint voltage of the faulty bridge is obtained as:

$$u_{coF1}<\frac{u_{dc}}{2},$$

(4)

The polarity J_xo of the midpoint voltage of the bridge x is defined as:

$$J_{xo}=J\left[u_{xoF}-u_{xoN}\right],$$

(5)

where u_xoF denotes the midpoint voltage after one power switch is fault at phase x. u_xoN is the normal midpoint voltage at phase x. x = (a, b, c). When V₁ is in an open-circuit fault and S_c = 1, according to Equations (2) and (4), there is the polarity J_co of the midpoint voltage of the bridge c:

$$J_{co1}=J\left[u_{coF1}-u_{coN1}\right]=N,$$

(6)

The difference of the midpoint voltage of the bridge before and after fault is less than 0. That is to say, this polarity of the voltage difference is negative N. The reconfiguration process after the fault of inverter 1. V₁ is removed is shown in Figure 2b. TR₄ is triggered on and stops sending triggering pulses to V₂. The phase c is replaced by the DC-side capacitors. The inverter can be reconstructed into the TPFS structure which is shown in Figure 2d. The first fault diagnosis and reconfiguration are finished.

Similarly, the polarity of the midpoint voltage of other bridges can be also obtained when other power switch faults occur. After the faulty power switch is diagnosed, the inverter can be reconfigured to operate in the fault-tolerant state. The results of the first fault diagnosis and reconstruction according to the polarity of the midpoint voltage difference of the bridge are shown in

Table 2. First fault diagnosis and reconfiguration.

Case	First Fault	Jao	Jbo	Jco	On
1–1	Normal	Z	Z	Z	TR3
1–2	V1	N	Z	Z	TR4
1–3	V2	P	Z	Z	TR4
1–4	V3	Z	N	Z	TR2, TR4
1–5	V4	Z	P	Z	TR2, TR4
1–6	V5	Z	Z	N	TR1, TR4
1–7	V6	Z	Z	P	TR1, TR4
1–8	V1 & V2	N-P	Z	Z	TR4
1–9	V1 & V3	N	N	Z	No
1–10	V1 & V4	N	P	Z	TR2, TR4
1–11	V1 & V5	N	Z	N	No
1–12	V1 & V6	N	Z	P	TR1, TR4
1–13	V2 & V3	P	N	Z	TR2, TR4
1–14	V2 & V4	P	P	Z	No
1–15	V2 & V5	P	Z	N	TR1, TR4
1–16	V2 & V6	P	Z	P	No
1–17	V3 & V4	Z	N-P	Z	TR2, TR4
1–18	V3 & V5	Z	N	N	No
1–19	V3 & V6	Z	N	P	No
1–20	V4 & V5	Z	P	N	No
1–21	V4 & V6	Z	P	P	No
1–22	V5 & V6	Z	Z	N-P	TR1, TR4

. The polarities J_ao, J_bo and J_co of the midpoint voltage of the bridges a, b and c. Z, N, and P represent zero, negative, and positive, respectively. “No” means it isn’t reconfigured. N-P presents the polarity of the midpoint voltage difference negative when the faulty switch is in the upper bridge and positive when the faulty switch is in the lower bridge.

Take case 1–1 as example. If V₁ is detected as faulty, the polarities J_ao is negative and J_bo and J_co are positive. Then the inverter 1 is reconfigured after the first fault so that the inverter 1 can operate fault-tolerantly. Some power switches can still be used after the reconfiguration in some fault cases. For example, when the faulty V₁ is removed, V₂ is still normal. Therefore, V₂ can be used for the second reconfiguration when the other power switch in the inverter is detected as faulty.

The primary reconfigured inverter as shown in Figure 2d is diagnosed for the second time. Then power switch V₄ is taken as an example. We can see from Figure 2d, when V₄ has no fault, the voltage of the midpoint of the bridge can be expressed as:

$$u_{boN2}=\left\{\begin{array}{l}\frac{u_{dc}}{2}\hspace{1em}\hspace{1em}{S}_b=1\\ -\frac{u_{dc}}{2}\hspace{1em} S_b=-1\end{array}\right.,$$

(7)

when V₄ has an open-circuit fault and S_b = −1, V₃ and V₄ are both disconnected, then point b is suspended and i_b = 0. Potential b is the same as potential n. That is u_boF = u_noF.

According to Figure 2d, when S_a = 1 and S_b = −1, there is the midpoint voltage u_boF after the second fault as:

$$u_{b\mathrm{oF}2}=u_{n\mathrm{o}F2}=\frac{u_{dc}}{2\times 2Z}\times Z=\frac{u_{dc}}{4},$$

(8)

when S_a = −1 and S_b = −1, there is:

$$u_{b\mathrm{o}F2}=u_{n\mathrm{o}F2}=-\frac{u_{dc}}{2\times 2Z}\times Z=-\frac{u_{dc}}{4},$$

(9)

Finally, considering Equations (7)–(9), there is:

$$J_{b\mathrm{o}2}=J\left[u_{noF2}-u_{noN2}\right]=P,$$

(10)

That is to say, when an open-circuit fault occurs at V₄, the polarity J_bo2 of the midpoint voltage difference of the bridge b is positive. The second reconfiguring process is shown in Figure 2c after the fault of V₄. V₄ is removed. TR₄ is triggered on and the pulse signal of V₄ is sent to V₂. The phase c is still replaced by the DC-side capacitors. The inverter can be still reconstructed into the TPFS structure which is shown in Figure 2d. The second fault diagnosis and reconfiguration are finished.

Similarly, the polarity of the midpoint voltage difference of other bridge can be obtained when other power switches fail. The results of the second fault diagnosis and reconfiguration are shown in

Table 3. Second fault diagnosis and reconfiguration.

Case	First Fault	Second Fault	Jao	Jbo	Jco	On
2–1	V1	V4	Z	P	Z	TR2
2–2	V1	V6	Z	Z	P	TR1
2–3	V2	V3	Z	N	Z	TR2
2–4	V2	V5	Z	Z	N	TR1
2–5	V3	V2	N	P	Z	TR2
2–6	V3	V4	Z	P	Z	/
2–7	V4	V1	P	Z	Z	TR2
2–8	V4	V3	Z	N	Z	/
2–9	V5	V2	P	Z	Z	TR1
2–10	V5	V6	Z	Z	P	/
2–11	V6	V1	N	Z	Z	TR1
2–12	V6	V5	Z	Z	N	/

. “/” means no need to let any other triacs be on. In Table 3, take case 2–1 as example. The inverter 1 is already reconfigured as TPFS when V₁ is detected faulty. The polarities J_bo is positive. TR₄ and TR₂ are triggered on and the pulse signal of V₄ is sent to V₂. The phase c is still replaced by the DC-side capacitors. The inverter 1 can be reconstructed into the TPFS again.

The secondary reconfiguration enables the inverter to continue operating in fault-tolerant mode and the fault tolerant space is greatly improved to make the system more reliable. We can see from the inference procedure that the second fault diagnosis is the same as the first. The fault diagnosis method can also diagnose dual power switches, which has strong universality. What’s more, the reconfigured bridge is always c-phase whichever power switch is faulty, which is convenient to design the control strategy.

2.3. The Control Strategy for The Off-Grid Microgrid

2.3.1. The Circulating Currents Analysis

In the off-grid microgrid shown in Figure 1, if the parameters between the two inverters are not completely consistent, the amplitude and phase of the output voltages are different, and the line impedances are unequal. The circulating currents between the parallel systems will be generated, resulting in the microgrid produces large losses, which will cause the inverter power switching devices to burn out in serious cases, and affect the stable operation of the entire microgrid. This section analyzes the circulating currents between the two inverters in Figure 1 to design the circulating current suppression strategy to make the microgrid operation safer and more stable. Figure 3 is a schematic diagram of the circulating currents between the inverter 1 and the inverter 2 after reconstruction.

From Figure 3, the output currents of inverter 1 and inverter 2 can be obtained as:

$$\left\{\begin{array}{l}{i}_{a1}=\frac{u_{dc}\left(2S_a-S_b-\frac{1}{2}\right)-3u_{PCC}}{3Z_{eq1}}\\ i_{b1}=\frac{u_{dc}\left(-S_a+2S_b-\frac{1}{2}\right)-3u_{PCC}}{3Z_{eq1}}\\ i_{c1}=\frac{u_{dc}\left(-S_a-S_b+1\right)-3u_{PCC}}{3Z_{eq1}}\end{array}\right.,$$

(11)

$$\left\{\begin{array}{l}{i}_{a2}=\frac{u_{dc}\left(2S_a-S_b-S_c\right)-u_{PCC}}{3Z_{eq2}}\\ i_{b2}=\frac{u_{dc}\left(-S_a+2S_b-S_c\right)-u_{PCC}}{3Z_{eq2}}\\ i_{c2}=\frac{u_{dc}\left(-S_a-S_b+2S_c\right)-u_{PCC}}{3Z_{eq2}}\end{array}\right.,$$

(12)

Among them, u_PCC is the voltage at the PCC point. The formula for calculating the circulating current between the two inverters is as follows:

$$i_{Hx}=\frac{i_{x2}-i_{x1}}{2},$$

(13)

where, i_x1 and i_x2 are the output currents of the two inverters respectively, x = a, b, c.

Assuming that the equivalent output impedances of the two inverters in the microgrid with reconfigurable inverters are equal, that is Z_eq1 = Z_eq2 = Z_eq. The circulating current of each phase between the reconstructed inverter 1 and inverter 2 is:

$$\left\{\begin{array}{l}{i}_{Ha}=\frac{u_{dc}\left(-4S_a+2S_b+3S_c-\frac{1}{2}\right)}{6Z_{eq}}\\ i_{Hb}=\frac{u_{dc}\left(2S_a-4S_b+3S_c-\frac{1}{2}\right)}{6Z_{eq}}\\ i_{Hc}=\frac{u_{dc}\left(2S_a+2S_b-6S_c+1\right)}{6Z_{eq}}\end{array}\right.,$$

(14)

It can be seen from the above equation that when the equivalent output impedances of the two inverters are the same, the magnitude of the circulating currents generated between the two inverters are affected by the modulation of the switching function. If the equivalent output impedances of the two inverters are inconsistent, the circulating currents will increase further. In order to ensure the safe and stable operation of the microgrid, the circulating currents must be suppressed.

2.3.2. Adoptable Virtual Impedance Based on the Cloudy Model

In order to make the equivalent output impedances of the inverter consistent, virtual negative resistance and virtual positive inductances are added to offset the circulation problem caused by unbalanced line impedances and reconstruction and make the equivalent output impedance purely inductive. In this paper, the virtual impedance is designed as:

$$Z_v=-R_v+j\omega L_v,$$

(15)

Among them, R_v is the virtual resistance and L_v is the virtual inductance. Under the function of R_v and L_v, the equivalent output impedances of the two inverters are adjusted, so that the equivalent output impedance balance is approximately purely inductive.

Since the circulating currents are always changing under the influence of the switching function, and the line impedances are constantly changing under the influence of the environment, the circulating current values are not fixed. If a fixed value of the virtual impedance is used to suppress the changing circulating currents, the suppression effect is poor. The traditional virtual impedance method to suppress circulating current has the characteristics of fixed virtual impedance value and low flexibility. The membership cloud model theory has excellent self-adjustment performance in intelligent control. So an adaptive virtual impedance acquisition algorithm based on the membership cloud model is proposed in this paper, as shown in Figure 4.

In Figure 4, the numerical input signals are the difference e and the deviation ec of the circulation current. The operating principle structure of the membership cloud model includes mainly three parts: cloudification which is used to cloud numerical input signal values, cloud uncertainty reasoning to get the expected output clouds based on uncertainty reasoning rules and obtaining numerical output signals.

The first step is cloudification that the numerical input signal values are clouded as follows. A random function R(E_x, σ) which follows a normal distribution is needed. Parameters E_x and σ in R(E_x, σ) are the expected value and the standard deviation, respectively. If E_n and H_e are used to denote the expected value and the standard deviation, respectively, a normal random entropy $E_n^{\prime }$ with E_n and H_e is obtained as:

$$E_n^{\prime }=R\left(E_n,H_e\right),$$

(16)

Then the cloud droplet $x_i$ is generated as:

$$x_i=R\left(E_x,E_n^{\prime }\right),$$

(17)

The membership function ${\mu }_i$ can be obtained from Equation (18) which satisfies the normal distribution form:

$${\mu }_i=\exp \left\{\frac{-{\left(x_i-E_x\right)}^2}{2{\left(E_n^{\prime }\right)}^2}\right\},$$

(18)

It means that the cloud droplet x_i has the degree of membership μ_i in Equation (18). A lot of cloud droplets form a cloud G(E_x, E_n, H_e).

From Figure 4 it can be seen that there are two input signals e and ec, which represent the circulating current difference and the deviation of the circulating current difference, respectively. The clouds of e and ec are expressed as e(E_x, E_n, H_e) and ec(E_x, E_n, H_e), which have seven clouds, respectively. Each digital characteristic is calculated by the golden section method [32].

Table 4. Digital characteristics for input signals.

e(Exe, Ene, Hee)	ec(Exec, Enec, Heec)
eNB(−10, 3.33, 0.42)	ecNB(−3, 0.89, 0.32)
eNM(−3.82, 2.06, 0.26)	ecNM(−1.21, 0.61, 0.23)
eNS(−1.91, 1.27, 0.16)	ecNS(−0.58, 0.19, 0.11)
eZ(0, 0.79, 0.1)	ecZ(0, 0.40, 0.05)
ePS(1.91, 1.27, 0.16)	ecPS(0.58, 0.19, 0.11)
ePM(3.82, 2.06, 0.26)	ecPM(1.21, 0.61, 0.23)
ePB(10, 3.33, 0.42)	ecPB(3, 0.89, 0.32)

shows the digital characteristics for input signals e and ec, respectively. The subscripts NB (negative big), NM (negative medium), NS (negative small), Z (zero), PS (positive small), PM (positive medium) and PB (positive big) are fuzzy language sets for the qualitative uncertainty reasoning.

From Figure 4 it can be seen that there are two output signals L_v and R_v. In the same way, the digital characteristics for output signals L_v and R_v can be obtained and are shown in

Table 5. Digital characteristics for output signals.

LV(ExL, EnL,HeL)	RV(ExR, EnR, HeR)
LV NB(−6 × 10−4, 2 × 10−4, 4.2 × 10−4)	RV NB(−2.5 × 10−2, 8.3 × 10−3, 8.4 × 10−4)
LV NM(−2.9 × 10−4, 1.2 × 10−4, 2.6 × 10−4)	RV NM(−9.5 × 10−3, 5.2 × 10−3, 5.2 × 10−4)
LV NS(−1.9 × 10−4, 0.76 × 10−4, 1.6 × 10−4)	RV NS(−4.8 × 10−3, 3.2 × 10−3, 3.2 × 10−4)
LV Z(0, 0.5 × 10−4, 1 × 10−4)	RV Z (0, 2 × 10−3, 2 × 10−4)
LV PS(1.9 × 10−4, 0.76 × 10−4, 1.6 × 10−4)	RV PS(4.8 × 10−3, 3.2 × 10−3, 3.2 × 10−4)
LV PM(2.9 × 10−4, 1.2 × 10−4, 2.6 × 10−4)	RV PM(9.5 × 10−3, 5.2 × 10−3, 5.2 × 10−4)
LV PB(6 × 10−4, 2 × 10−4, 4.2 × 10−4)	RV PB(2.5 × 10−2, 8.3 × 10−3, 8.4 × 10−4)

.

The second step is that the cloud uncertainty reasoning rules are designed. Because there are two input signals e and ec, the biconditional rules are needed here, which is shown in Figure 5. For example, If e = e_PB and ec = ec_PB, then Z_i = L_vPB.

In Figure 5, CG_A is the forward two-dimensional cloud generator. Here cloud generator is represented as CG. It is built from three pairs of digital feature values ((E_xe E_xec), (E_ne E_nec), (H_ee, H_eec)), and it satisfies:

$$\mu \left(e,ec\right)=\exp \left(\frac{-{\left(e-E_x{}_e\right)}^2}{2{\left(E_{\mathit{ne}}^{\prime }\right)}^2}+\frac{-{\left(ec-E_x{}_{ec}\right)}^2}{2{\left(E_{\mathit{nec}}^{\prime }\right)}^2}\right),$$

(19)

Here $E_n{}_e^{\prime }=R\left(E_n{}_e,H_e{}_e\right)$ and $E_n{}_{ec}^{\prime }=R\left(E_n{}_{ec},H_e{}_{ec}\right)$. CG_B is the reverse one-dimensional cloud generator with digital characteristic values (E_xi, E_ni, H_ei), and it satisfies:

$$Z_i=E_x{}_i\pm \sqrt{-2\ln \left[\mu \left(e,ec\right)\right]}{E}_{\mathit{ni}}^{\prime }$$

(20)

Here $E_{\mathit{ne}}^{\prime }=R\left(E_n{}_i,H_e{}_i\right)$. When the deviation e < E_xe, the ± in (20) takes a negative signal, otherwise it is a positive sign+. Z_i is the numerical output signal value.

In Figure 6, it can be seen that the membership cloud model has i (i = 1, 2,…, n) biconditional rules and n = 49 here. The input signals e and ec stimulate different forward two-dimensional cloud generators CG_Ai to generate membership μ_Ai, then μ_Ai pass through the reverse one-dimensional cloud generators CG_BLi and CG_BRi to generate a large number of numeric outputs Z_Li and Z_Ri to get the virtual impedance L_v and R_v, respectively. The final numeric outputs L_v and R_v are calculated by the weighted average value of m Z_Li and Z_Ri, respectively as:

$$L_v=\frac{{\displaystyle \sum _{i=1}^m{Z}_{Li}{\mu }_{Ai}}}{{\displaystyle \sum _{i=1}^m{\mu }_{Ai}}},$$

(21)

$$R_v=\frac{{\displaystyle \sum _{i=1}^m{Z}_{Ri}{\mu }_{Ai}}}{{\displaystyle \sum _{i=1}^m{\mu }_{Ai}}},$$

(22)

2.3.3. The General Control Strategy

Figure 7 is the general control strategy of the off-grid microgrid. The control strategy connecting droop-voltage-current three-loop with virtual impedance based on the membership cloud model is applied in inverter 2, which is shown in the green dashed box.

The control schematic of the reconfigurable inverter 1 in off-grid microgrid is shown in the red dashed box. When inverter 1 is diagnosed without fault and it runs in normal state, inverter 1 only uses the control strategy connecting droop-voltage-current three-loop with virtual impedance based on the membership cloud model, which is also adopted in inverter 2. The virtual impedance voltages in dq coordinates can be obtained as:

$$\left\{\begin{array}{c}{u}_{vd}=i_{od}\cdot (-R_v)-i_{oq}\omega L_v\\ u_{vq}=i_{oq}\cdot (-R_v)+i_{od}\omega L_v\end{array}\right.,$$

(23)

In Equation (23), i_od, i_oq are in the dq coordinatea for the output currents i_o. ω is the public point voltage frequency. The pulse-resetting is needed when inverter 1 is diagnosed faulty and it runs in faulty state, which is shown in red dashed box. The final pulses T_v1–T_v6 can be obtained for the power switches in inverter 1.

3. Results and Discussion

3.1. Simulating Results and Analysis

The model of the off-grid microgrid with the proposed twice reconfigurable inverter with twice fault diagnosis based on Figure 1 is built in Matlab Simulink as shown in Figure 8.

The main simulation parameters are given in

Table 6. The main parameters of the simulation model.

Main Paramenter	Value
Given voltage value Um	380 V
Given voltage frequency f	50 Hz
The DC side voltage of inverter 1 and 2	800 V
The switch frequency of IGBT	10 k/Hz
The filter inductance L1 The filter capacitance C	3 mH 5000 μF
The filter inductance L2	3 mH
km and kn of droop control	1 × 10−5, 4× 10−5

. Two inverters have the same parameters.

All four operating modes are simulated. The simulation time is 2 s.

3.1.1. Operating Mode 1

In the operating mode 1, both inverters work normally. The simulation results are given in Figure 9.

From the operating model simulation results shown in Figure 9 it can be seen that the output voltages and currents of two inverters are equal, with the same amplitude and frequency, which have normal shapes.

3.1.2. Operating Mode 2

In operating mode 2, inverter 1 is good while inverter 2 is removed because of breaking down at t = 1 s. These simulation results are shown in Figure 10.

From Figure 10, we can see that the values of output currents in inverter 1 are double the original values at t = 1 s, because inverter 2 is removed. Meanwhile the output voltage waveforms of inverter 1 are kept the same before and after inverter 2 fails, which is same situation as in Figure 9a. The simulation results of the inverter 2 are not given here because it is removed after it failed. The voltages of inverter 1 can be supported by the capacitors in the filter LCL and there is the voltage control in the control strategy, so there are no noticeable changes in the voltages.

3.1.3. Operating Mode 3

In operating mode 3, both inverters are considered to have failed at t = 1 s. At this moment, inverter 2 is removed while inverter 1 is reconfigured. Inverter 1 is faulty again at 1.2 s.

There is a different faulty power switch in inverter 1 at t = 1 s and 1.2 s, respectively. The polarities of the inverter 1 midpoint are shown in Figure 11a. The output voltages of inverter 1 are maintained the same good shapes before or after the fault, as are the output currents. However, because inverter 2 is faulty and it is removed at 1 s, the original power of inverter 2 is transferred to inverter 1. Meanwhile the value of output currents in inverter 1 increases. Although inverter 1 has the second fault at 1.2 s, its output voltages and currents can still return good waveforms. From these simulation results, the proposed reconfigured structure and the pulse-resetting for inverter 1 is verified and the microgrid can work continuously under faulty inverter 1 conditions.

3.1.4. Operating Mode 4

In operating mode 4, at t = 1 s inverter 1 is the first fault and it is the second fault at t = 1.2 s. Inverter 2 is operating normally all the time. The simulation results in Figure 12b,d are almost same as those in operating mode 1. The output voltages and currents of inverter 1 kept good shapes before and after the fault, although inverter 1 is reconfigured twice at t = 1 s and t = 1.2 s, respectively. Because inverter 2 has no fault, these output voltages of inverter 2 are the same in all time. The output currents of two inverters are same whether they work in normal or faulty states, there is hardly any circulation current between the two inverters because of the virtual impedance obtained from the cloud model. The proposed virtual impedance based on the cloud model is verified to suppress the circulation currents between inverters.

3.1.5. Operating Model without Reconfigured Structure

Inverter 1 and inverter 2 have completely the same structure and control strategy in this simulating model. There is not reconfigured structure and corresponding pulse-resetting in inverter 1. V₁ in the inverter 1 is faulty at t = 0.5 s. Inverter 2 works in the normal state. The simulation results are shown in Figure 13.

According to Figure 13, the output current waveforms of inverter 1 and inverter 2 are distorted and three-phase imbalanced when inverter 1 is faulty. The circulating current is increased greatly. That is to say, the microgrid can’t work in its normal state because inverter 1 is faulty. The proposed reconfigured structure and corresponding control strategy can improve greatly the reliability of the microgrid.

From all the simulation results, we can see that the output voltages and currents in operating modes 2 and 3 are similar, because inverter 1 is reconfigured to have the fault-tolerant function. The output voltages and currents in operating modes 1 and 4 are also similar. It means that if inverter 1 is reconfigured after one or two power switches are in open circuit fault, there is at least one inverter operating continuously in the off-grid microgrid. In operating mode 1, this is a normal operating mode. Because all parameters of the two inverters are same, there is no circulation current between them. In operating modes 2 and 3, only inverter 1 is working after fault, there is no need to discuss circulation currents. In operating mode 4, Figure 12f shows the circulating currents hardly run between the two inverters, whereby the intelligent control strategy is verified. The simulation results without the proposed reconfigured structure and corresponding control strategy are given, which are distorted and imbalanced if inverter 1 is faulty. Compared these results, it is obvious that the reliability of the off-grid microgrid is greatly improved under the proposed reconfigured structure and control strategy.

4. Conclusions

An intelligent control strategy for a highly reliable microgrid in off-grid mode with a twice reconfigurable inverter and its fault diagnosis is proposed in this paper. The fault diagnosis method and the reconfiguration can be used twice for inverter 1. What’s more, the reconfigured bridge is always c-phase whichever power switch is faulty, which is good to design the control strategy. The fault-tolerant workspace is large. The circulating currents between the two inverters are analyzed. According to the circulating currents, the virtual impedance based on the membership cloud model is proposed to suppress the circulating currents. A pulse resetting method is adopted, which makes changing the control algorithm before or after the inverter 1 is reconfigured unnecessary, so an intelligent control strategy containing four control loops is formed: the droop control loop, the virtual impedance based on the membership cloud model loop, voltage-current control loop and pulse resetting. Finally, a simulation model is built. The simulation results verify the feasibility of the topology, the fault diagnosis method and the control strategy of the off-grid microgrid with the twice reconfigurable inverter.